Science:Math Exam Resources/Courses/MATH102/December 2011/Question 04 (ii)
• Q1 (a) i • Q1 (a) ii • Q1 (b) i • Q1 (b) ii • Q1 (b) iii • Q1 (c) • Q2 (a) i • Q2 (a) ii • Q2 (a) iii • Q2 (b) i • Q2 (b) ii • Q2 (b) iii • Q2 (c) • Q3 • Q4 (i) • Q4 (ii) • Q4 (iii) • Q4 (iv) • Q4 (v) • Q4 (vi) • Q5 • Q6 • Q7 (i) • Q7 (ii) • Q7 (iii) • Q8 (i) • Q8 (ii) • Q8 (iii) • Q9 •
Question 04 (ii) 

Consider the function ii) Find the values of all the local maxima and minima of . Note: if maxima or minima do not exist, say so. 
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Hint 

Local extrema occur potentially at critical points. Find them and then justify whether or not they are local extrema. 
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Solution  

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Please rate my easiness! It's quick and helps everyone guide their studies. Taking the derivative gives Which allows to write a sign table for the derivative. And so we see that the function is decreasing up to x = 0, where it has a global minimum and then is increasing. 